Functional Analysis and Distribution Theory

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Related lectures (32)

Page 1 of 4

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Dual Spaces: Definitions and Properties

Covers the definitions and properties of dual spaces and linear operators.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.